Faculté des sciences

Linear rational finite differences from derivatives of barycentric rational interpolants

Klein, Georges ; Berrut, Jean-Paul

In: SIAM Journal on Numerical Analysis, 2012, vol. 50, no. 2, p. 643–656

Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a... Plus

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    Summary
    Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a special case and are more stable for calculating one-sided derivatives as well as derivatives close to boundaries.